Is that the maximum in the range $[-9,9]$? Why make that cutoff?
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AaronMay 31 '11 at 17:35

[-9,9] is arbitrary. Any non-tangent line going through two rational points on an elliptic curve will go through a third. Multiplying by the GCD gives an elliptic curve going through more integer lattice points, for a sufficiently large lattice. I was wondering about maxima on a small lattice, so I picked [-9,9] arbitrarily.
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Silas PikeMay 31 '11 at 20:43

1 Answer
1

This is a bit of a longshot, but have a look at Matthew Baker and Clayton Petsche, Global discrepancy and small points on elliptic curves, http://arxiv.org/pdf/math/0507228v1 and at some of the papers in the references that have titles that suggest they may be relevant to this problem.